Claim record · edition 0.1.0
The reading of a MERA network as a discretized holographic geometry is a proposed correspondence, not a derived one, and published work argues its consistency conditions are in tension.
The proposal observes that the extra layer direction of a MERA behaves like a radial bulk coordinate and that entanglement entropy has a geometric reading in the network. Subsequent work set out conditions such a correspondence would have to satisfy and argued they conflict.
Limits of this claim
This atlas records the conjecture and the objection; it does not adjudicate them. Critically, no numerical use of MPS, MERA, or PEPS as an optimization method depends on the correspondence being true — the algorithms predate it and stand on their own analysis. Treating the holographic reading as a warrant for a computational claim is a category error.
Supporting sources
primary paper · identifier verified
Entanglement Renormalization and Holography
Brian Swingle · 2009
arXiv:0905.1317
The paper that proposed reading the MERA network as a discretized holographic geometry. It is the origin of the AdS/MERA conjecture, not a proof of it.
Source record →primary paper · identifier verified
Consistency Conditions for an AdS/MERA Correspondence
Ning Bao, ChunJun Cao, Sean M. Carroll, Aidan Chatwin-Davies, Nicholas Hunter-Jones, Jason Pollack, Grant N. Remmen · 2015
arXiv:1504.06632
States conditions an AdS/MERA correspondence would have to satisfy and argues they are in tension. It is why tn-005 is labelled a conjecture rather than a result.
Source record →